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On upper bounds for the variance of functions of random variables with weighted distributions

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Abstract

Cacoullos and Papathanasiou (1989) obtained a characterization for the distribution of a random variable via the upper bounds for the variance of a given function of that random variable. In this paper, on the basis of their works, we derive a characterization for the weighted distribution. Subsequently, by using the characterization and in terms of Chernoff-type inequalities, we find the upper bounds for the variance of a given function of the weighted random variable. Moreover, assuming that X is IFR [increasing failure rate] we compute an upper bound for the variance of this function.

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Authors and Affiliations

  1. Department of Statistics, Ferdowsi University of Mashhad, P. O. Box 1159, Mashhad, 91775, Iran

    F. Goodarzi, M. Amini & G. R. Mohtashami Borzadaran

Authors
  1. F. Goodarzi
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  2. M. Amini
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  3. G. R. Mohtashami Borzadaran
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Correspondence to F. Goodarzi.

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Submitted by Andrei Volodin

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Goodarzi, F., Amini, M. & Mohtashami Borzadaran, G.R. On upper bounds for the variance of functions of random variables with weighted distributions. Lobachevskii J Math 37, 422–435 (2016). https://doi.org/10.1134/S1995080216040089

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  • DOI: https://doi.org/10.1134/S1995080216040089

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